Why are there borders around faces when I extrude?
If you create a new file, create a cube, or use default one, subdivide it, select some faces and hit E only once for every time you want to extrude, there should be no borders around the extrusion:

It would be a common beginner mistake to press E a few times this way creating more extrusions so this might be it. You could just start over from scratch since this is not very complex and the objective here is probably more to learn then to save a few minutes.